Probabilistic Assumption-Based Reasoning

In this paper the classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then the whole model is placed into the framework of the Dempster-Shafer theory of evidence. Laskey, Lehner [1] and Provan [2] have already proposed a similar point of view but these papers do not emphasize the mathematical foundations of the probabilistic assumptionbased reasoning paradigm. These foundations are thoroughly exposed in the rst part of this paper. Then we address the computational problems related to the assumption-based model. The idea is to translate evidence theory problems into propositional logic problems and then use the powerful techniques of logic to solve them. In particular, advanced consequence nding algorithms developed by Inoue [3] and Siegel [4] will be used. These logic-based techniques can be considered as alternatives to the classical method of local propagation in Markov trees. Finally, we switch back from logic to the theory of evidence in order to compute degrees of support of hypotheses. We show that some recently proposed methods for computing simple disjunctive normal forms can be used to compute these degrees of support.